Subsystem dynamics under random Hamiltonian evolution

Details Subsystem dynamics under random Hamiltonian evolution Subsystem dynamics under random Hamiltonian evolution

2011-07-29

arxiv.org/abs/1107.6035v3

J. Phys. A: Math. Theor. 45, 125204 (2012)

Physics

Quantum Physics

16 pages, 8 figures; v3: slightly re-structured and an additional appendix

Scientific paper

10.1088/1751-8113/45/12/125204

We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and fluctuations. We show that the reduced density matrix can be described in terms of a noncentral correlated Wishart ensemble for which we are able to perform analytical calculations of the eigenvalue density. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.

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